A NEW METHOD FOR ANALYZING IMAGES AND TIME SERIES USING A POTENTIAL TRANSFORMATION 

Butusov Oleg Borisovich, doctor of physical and mathematical sciences, professor, sub-department of mathematics, Moscow Polytechnic University (107023, 38 B. Semenovskaya street, Moscow, Russia), E-mail: butusov-1@mail.ru
Dikusar Vasily Vasilevich, doctor of physical and mathematical sciences, professor, chief researcher of the Department of security and non-linear analysis, Federal Research Center for computer science and management of the Russian Academy of Sciences (Computing Center, A. A. Dorodnicyna RAS) (119333, 40 Vavilov street, Moscow, Russia); professor, sub-department of higher mathematics, Moscow Institute of Physics and Technology (State University) (141701, 9 Institutsky lane, Dolgoprudny, Moscow region, Russia), E-mail: dikussar@yandex.ru 

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10.21685/2307-4205-2019-1-2 

A new method of time series and image transformation similar to the method of image analysis using remote transformations is proposed. The method is characterized by the fact that the transformation is not used distances between binary points, and their nonlinear combinations of formulas, which are similar in structure to the calculation formulas of different types of potential energy. The essence of the method is as follows. The first step uses binarization of the original black-and-white image or time series. Further binary pixels (binary image points) are considered as interacting pseudo-particles. The conversion is performed using a sliding window. For each position of the sliding window, a pseudopotential is calculated, which is written to the center point of the window. Two types of pseudopotentials are considered: the potential of the spin-spin Ising interaction and the Coulomb potential. For time series, calculations were performed at different values of the sliding window width. The combination of the results was presented as a twodimensional image. The results of this 1-D to 2-D transformation showed that the potential transformation gives more detailed information about the hidden patterns compared to the continuous wavelet transform. 

time series, images, continuous wavelet transform, Ising potential, Coulomb potential, binarization, normalization, time series purification from emissions